Casimir forces are a manifestation of quantum vacuum fluctuations at the macroscopic level and are important also in a cosmological context for their potent contribution to the cosmological constant. We report on the measurement of the Casimir force between conducting surfaces in a parallel configuration. The force is exerted between a silicon cantilever coated with chromium and a similar rigid surface and is detected by looking at the shifts induced in the cantilever frequency when the latter is approached. The scaling of the force with the distance between the surfaces was tested in the 0.5-3 mum range and the related force coefficient was determined at the 15% precision level. The measurement technique can also be used to look at new physics related to gravitation in the submillimeter range.